Axiomatising the dagger category of complex Hilbert spaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911278624145408 |
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| author | Paseka, Jan Vetterlein, Thomas |
| author_facet | Paseka, Jan Vetterlein, Thomas |
| contents | We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of objecs, two further ones deal with the decomposition of objects, and a final axiom expresses a symmetry property.
The categorical reconstruction of complex Hilbert spaces addresses foundational issues in quantum physics. We present a simplified alternative to recent characterisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Axiomatising the dagger category of complex Hilbert spaces Paseka, Jan Vetterlein, Thomas Category Theory Quantum Physics 81P10, 18M40, 46C05 We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of objecs, two further ones deal with the decomposition of objects, and a final axiom expresses a symmetry property. The categorical reconstruction of complex Hilbert spaces addresses foundational issues in quantum physics. We present a simplified alternative to recent characterisations. |
| title | Axiomatising the dagger category of complex Hilbert spaces |
| topic | Category Theory Quantum Physics 81P10, 18M40, 46C05 |
| url | https://arxiv.org/abs/2511.15410 |